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The Buzzard-Diamond-Jarvis conjecture for unitary groups

Authors: Toby Gee, Tong Liu and David Savitt
Journal: J. Amer. Math. Soc. 27 (2014), 389-435
MSC (2010): Primary 11F33, 11F80
Published electronically: July 3, 2013
MathSciNet review: 3164985
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Abstract: Let $ p>2$ be prime. We prove the weight part of Serre's conjecture for rank two unitary groups for mod $ p$ representations in the unramified case (that is, the Buzzard-Diamond-Jarvis conjecture for unitary groups), by proving that any Serre weight which occurs is a predicted weight. Our methods are purely local, using the theory of $ (\varphi ,\hat {G})$-modules to determine the possible reductions of certain two-dimensional crystalline representations.

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Additional Information

Toby Gee
Affiliation: Department of Mathematics, Imperial College London, London, SW7 2AZ United Kingdom

Tong Liu
Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907

David Savitt
Affiliation: Department of Mathematics, University of Arizona, 617 N. Santa Rita Avenue, Tucson, Arizona 85721-0089

Received by editor(s): July 5, 2012
Received by editor(s) in revised form: May 15, 2013
Published electronically: July 3, 2013
Additional Notes: The second author was partially supported by NSF grant DMS-0901360.
The third author was partially supported by NSF grant DMS-0901049 and NSF CAREER grant DMS-1054032.
Article copyright: © Copyright 2013 American Mathematical Society

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